Discretion and Destruction: Promotions,Performance, and Patronage in the Royal Navy∗

Joachim VothUniversity of Zurich

& CEPR

Guo XuUniversity of California,

Berkeley Haas

First version: February 20, 2019This version: November 13, 2020

Abstract

Both rules and discretion can be used in hiring and promotion decisions. How effec-tive is discretion in making appointments to important leadership positions? To an-swer this question, we collect new data on the performance of more than 5,800 navalofficer serving in the 18th century Royal Navy. From the choice set of all potential pro-motees, each year the Admiralty, at its discretion, chose a small number of officers tobecome “post-captain” – tenured officers who commanded major warships. Officersfast-tracked for promotion on average performed markedly better than those “passedover” – the Navy picked future winners. Selection was particularly effective for offi-cers connected to the Admiralty through family ties – first-hand personal knowledgeimproved promotion decisions. We construct counterfactuals for the fighting recordsof those who would have been chosen by alternative promotion rules, and find that dis-cretion in promotions outperformed them.

∗We thank Douglas Allen, Abhay Aneja, Charles Angelucci, Sascha Becker, Oriana Bandiera, ErnestoDal Bo, Fred Finan, Anderson Frey, Ruixue Jia, Danielle Li, Jin Li, Saumitra Jha, Peter Leeson, NicholasRodger, Laura Schechter, Edoardo Teso, and Noam Yuchtman for helpful discussions. Seminar audiencesat the Kellogg-Harvard PED Conference, Monash, UZH Faculty Lunch, the BGSE Summer Forum, and theUC Berkeley Economic History seminar provided valuable feedback. Noah Sutter, Caitlyn Schwartz, andHaoran Gao provided excellent research assistance.

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1 Introduction

Promotion decisions are key in many organizations (Prendergast, 1999). The more auton-omy employees enjoy, and the larger their span of control, the greater the importance ofpersonnel selection. Decision makers face a fundamental prediction problem: they mustselect future performers based on information available today (Bergman et al., 2020; Chalfinet al., 2016). Many firms and public sector organizations rely on rules based on senior-ity or measured output to promote employees. Such rules have the benefit of simplicityand transparency, but can lead to poor choices if important additional information is over-looked, or if past performance is a poor predictor of post-promotion performance (Bensonet al., 2019). The alternative – to leave the decision to those with better information – givesrise to the classic delegation problem: private information can be used to improve selection(Burks et al., 2015; Prendergast and Topel, 1996; Allen, 2011), or it can result in favoritismfor private gain (Xu, 2018; Colonnelli et al., 2018).

Whether discretion in promotion decisions works better than rules is ultimately an em-pirical question. Existing work has focused on lower-tier employees, and finds that discre-tion on average reduces the quality of personnel selection (Hoffman et al., 2018; Estrada,2019). However, leading large, complex organizations may require different skills than ju-nior positions (Stogdill, 1974; Northouse, 2018). The trade-off between discretion vs rulesmay therefore differ for leadership positions – the personnel decisions that arguably mat-ter the most for organizational performance (Cattell and Stice, 1954). There are three mainchallenges in assessing the value of discretion in promotions: First, the availability and useof private information are rarely observed. Second, most empirical settings only use infor-mation the final selection, but not the choice set. Without information on who could havebeen promoted and was passed over, it is hard to assess whether those actually promotedindeed outperform those not chosen. Third, good performance measures (before and afterpromotion) are rare in many organizations.

In this paper, we examine the value of discretion in promotions. We are the first todemonstrate that discretion can significantly improve selection and hence, overall per-formance. We study the promotion of captains in the Royal Navy during its eighteenth-century heyday, when it propelled Britain’s rise to global power (Kennedy, 2010). Captainsled warships of up to 950 men into battle. In every year, death, incapacity, retirement, andexpansion created openings. Accordingly, the Admiralty promoted new captains from thelist of lieutenants.1 Promotion gave new captains independent command of large ships,

1Connections to the very top were crucial because all promotions to “post” rank had to be confirmed by

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substantially increasing their autonomy and span of control.2 Promotion decisions were ir-reversible and consequential; just like the selection of chief executives or senior-level man-agers today, identifying who had the “right stuff” to lead was a difficult screening problem.Both character and skill mattered – appointing a coward to independent command was asure way of courting disaster. At the same time, favoring relatives and the offspring offriends was a constant temptation for senior admirals in an age when patronage at all lev-els of society was common (Rodger, 2005). We study whether the Admiralty Board – whichenjoyed full discretion in promotions – used private information to select better leaders, orabused the power of public office through favoritism.

Our study is based on the construction of a new, granular dataset. We assemble a yearlypanel for the period 1690–1849 covering the universe of British naval officers and warships.The resulting “matched captain-ship” dataset contains information on 5,848 officers as-signed to 3,904 ships. This dataset allows us to track the career progression of all officers.In each year, we can identify who was promoted and who was not – we observe the entirechoice set as well as the actual promotion decisions. This allows us to evaluate a total of2,782 promotion decisions made by 49 different Admiralty Boards.

To measure performance, we exploit rich data on the success of promoted officers. Anofficer’s principal objective was to capture, sink or burn enemy warships. These eventswere well recorded and weighted heavily in promotion decisions. Our measure of perfor-mance is the combined number of captures and enemy ships destroyed (”victories”). Weproxy private information with family connections, collecting data on family ties betweennaval officers and the two most senior naval leaders – the First Lord of the Admiralty andthe Admiral of the Fleet – from a large genealogical database. Since lineage was importantin 18th century society, family links mattered greatly.3

Promotion decisions can only be evaluated if the counterfactual is known – the perfor-mance of those not chosen (Kleinberg et al., 2018). This is rarely observed. A unique featureof our setting allows us to solve this problem: discretion in promotion decisions mainlyaccelerated the transition to captain. The majority of all officers were eventually promoted.

the Admiralty in London. Nonetheless, officers also received patronage from their commanding captain andadmiral (Malcomson, 2007).

2Prior to being made “post,” naval officers were typically employed in junior roles – for instance, as lieu-tenants serving under a captain in overall command. Only when assigned to small (“unrated”) ships did theyhave command of a vessel. After being made “post,” naval officers had much greater prospects of being as-signed a ship and received automatic promotions to larger vessels based on seniority. In contrast, lieutenantshad little employment security, received no automatic promotions, and commanded at best a small ship.

3Private information can come from a variety of sources. We only use family ties because they allow usto measure information asymmetries at a distance of more than two centuries.

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We therefore compare the performance of newly-minted captains with the eventual post-promotion performance of officers initially “passed-over.” If immediately promoted offi-cers perform markedly better than those ”passed-over,” selection decisions improved theRoyal Navy’s effectiveness. We compare this selection effect among candidates either con-nected or unconnected to the Admiralty. The resulting difference-in-difference estimatenot only purges time-specific shocks (which may confound a simple comparison betweenearly vs late promotion), but also allows us to isolate the role of private information inshaping selection.4 If admirals favored kin that went on to perform poorly, discretion inhiring would have reduced the Royal Navy’s fighting power. If, instead, they picked future”winners” thanks to better information, the opposite will be true. We introduce a simpleconceptual framework to pin down when discretion improves selection, and establish theconditions under which the post-promotion performance of later promotees can serve asa valid counterfactual to identify the selection effect.

Our results suggest that the Admiralty Board used private information to select higher-performing officers. In general, the Admiralty promoted based on lieutenants’ fightingrecords. Promotions were even more merit-based among officers connected to the Ad-miralty. Importantly, our analysis shows that promoted and ”passed-over” officers per-formed differently. While the pre-promotion capture rates of both groups were similar,those chosen for promotion immediately began to capture enemy vessels at a high rate,and continued to do so for several years. In contrast, the passed-over officers – candidatesnot chosen for immediate promotion by the Admiralty – had markedly less success, oncepromoted. In other words, admirals at the top of the Navy hierarchy on average selectedmen who were better at their job than those not favored straight away. Crucially, selectionwas particularly effective for connected officers. Connected officers not promoted by a rel-ative made merely average captains, but those raised rapidly to the rank of captain wenton to capture many enemy ships. We argue that this differential reflects private informa-tion – admirals could assess relatives’ probable performance better than that of strangers.For unconnected officers, in contrast – where the promoting admirals had less private in-formation – the difference in performance between promoted and passed-over officers ismarkedly smaller than for connected officers.

Promoting the right officers was genuinely difficult: the predictive power of regressionsof post-promotion performance on observables at the time of promotion is low. When con-trolling for all differences pre-promotion, the association between connectedness and per-

4In addition, it allows us to difference out any demotivating effect of being ”passed over,” which wouldapply to both connected and unconnected officers.

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formance remains strong and highly significant – suggesting that whatever informationallowed admirals to pick better captains went beyond their observable (pre-promotion)service record. Even when we flexibly balance the joint distribution of pre-promotion ob-servables between connected and unconnected officers using coarsened exact matching(CEM), we cannot “explain away” the superior selection of connected officers. This is con-sistent with private information driving the superior selection.

For a subset of our data, we can focus on ship-to-ship engagements, with a British war-ship fighting an enemy vessel. For these naval fights, we measure the fighting power (ap-proximated by the number of guns) of both ships. British ships in general won more ofteneven when outgunned, but the British advantage was particularly pronounced for officerspromoted by a relative at the Admiralty. The selection effect – the difference in fighting per-formance between early and late promotees – was much smaller for unconnected officers.

A key advantage of our empirical design is that we can calculate the counterfactual per-formance of promotees under alternative promotion rules. Compared with a wide range ofalternatives, actual practice performed relatively well. Had Royal Navy captains been pro-moted based on seniority alone, performance would have been markedly poorer – leadingto fewer captures of enemy ships. Actual promotions did much better than random pro-motions. A selection system based on merit would have performed better than random orseniority-based promotion – but it would not have outperformed actual selection practice.To derive an upper bound on selection effects, we perform a machine learning exercise us-ing random forest estimation. With this, we predict the capture rate of officer candidatesbased on observable characteristics. While the random forest model selects better officerson average than actual practice, the gap is not large – Royal Navy practice captures aroundthree quarters of the maximum gains from selection.

Finally, we examine the source of performance gains due to discretion by studyingwhen deviations from strict merit promotions are particularly effective. To do so, we com-pare the contributions of ”fast-tracking” vs filtering – favoring relatives, or holding themback. On average, navy performance improved when admirals advanced a relative (whenmerit-based promotion rules would not have suggested a promotion); they also improvedperformance when they ”passed over” a relative (when a merit-based promotion rulewould have suggested a positive decision). Both factors play a role, but fast-tracking’s con-tribution was somewhat greater. Actual practice in the Royal Navy outperformed merit-based selection between the Admiralty had discretion to ignore what a strict merit-basedpromotion rule would imply; where the admirals had superior information about candi-dates, this improved selection.

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Our results contribute to the literature on selection and incentives in public organiza-tions (Khan et al., 2015; Ashraf et al., 2016; Weaver, 2018; Ager et al., 2019; Bertrand et al.,2019; Khan et al., 2019). Rational and complex military organizations, such as the RoyalNavy, foreshadowed the emergence of professionalized bureaucracies. Indeed, conceptssuch as meritocracy (often associated with “Weberian” bureaucracies) first emerged in themilitary. Although a range of papers show that homophily matters for the allocation ofpositions (see e.g. Azulai, 2017; Do et al., 2017), there is little systematic evidence on howit affects performance. Exceptions include Xu (2018), who shows that patronage discour-aged favored colonial bureaucrats from raising revenue; Colonnelli et al. (2018), who reportthat winning municipal mayors in Brazil employ less qualified personnel from their poolof supporters;5 Lott (2013), who establishes that political influence reduces the quality ofjudges appointed to the bench in the United States; and Fisman et al. (2018), who demon-strate that scholars at the Chinese Academy of Science have less distinguished curriculavitae when they share hometown ties with admissions committee members. In contrast,evidence on the positive effects of discretion, including in family firms, are much morefrequent in the private sector (Bertrand and Schoar, 2006; Fisman et al., 2017).6 Our resultsalso resonate with the literature on the selection effects of CEOs (Bertrand, 2009).7

We also relate to the historical literature on the Royal Navy. Historians have long at-tributed its superior performance to Britain’s financial might: building, staffing, and main-taining large fleets and then supplying them effectively on the high seas for years (Dull,2009; Rodger, 2005). Although most of the literature is descriptive, economic analyses ofnavy performance have stressed the role of high-powered incentives for officers and alsofor seamen (Allen, 2002), such as severe penalities for failure, the payment of substantialprize money (Benjamin, 2005), promoted men from the lower deck as a result of perfor-mance (Benjamin and Thornberg, 2007), and successfully solved incentive problems in theprovisioning of food for the crews (a.k.a. the victualling) of its large fleets (Allen, 2018).The Royal Navy also improved more rapidly over time than its rivals, gathering more ex-perience in naval warfare and arguably learning more from it (Benjamin and Tifrea, 2007).We similarly conclude that the Royal Navy’s carefully balanced system of incentives fig-

5Brollo et al. (2017) document that, in closely contested elections’ in Brazil, the winning party hires moreof its own members – who are no less qualified (on average) than members of the opposition party.

6The exception is Hoffman et al. (2017); these authors find that private sector managers who ignore testrecommendations hire (low-skilled) service workers that end up having shorter tenures.

7Finally, our result that the less constrained selection of leaders can lead to greater variance in performanceechoes the findings of Jones and Olken (2005), who show that more autocratic regimes experience moreuneven growth.

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ured prominently in its success. Yet for that system to work, the right men had to be incommand because real-time monitoring was de facto impossible (Allen, 2002). We explorethe role of discretion in selecting them.

Finally, understanding promotions in the public sector is crucial because it influencesstate capacity (Rauch and Evans, 2000; Dal Bo et al., 2013; Finan et al., 2017). This papercontributes to our understanding of the origins of state capacity. A growing literature hasemphasized the importance of military competition for state building (Tilly, 1990; Besleyand Persson, 2010) and pointed out that many of today’s underdeveloped countries arelocated in areas with few interstate conflicts (Herbst, 2014). Contributions to the state-building literature have typically focused on the growth of taxation (Besley and Persson,2010; Gennaioli and Voth, 2015). Our findings demonstrate the importance of employeeselection for state capacity.

2 Historical background

In this section we summarize the Royal Navy’s organization, promotion system, and offi-cers’ incentives. We also identify the primary determinants of success in the “Age of Sail”and discuss the nature of private information used in promotion decisions.

2.1 Size and organization

The Royal Navy has its origins in the armed merchant ships that fought at the behest ofEnglish kings and queens. The Spanish Armada’s attempted invasion of England was de-feated mainly by converted merchant ships (Rodger, 1999). Britain’s Parliament in 1649 au-thorized the first large-scale program for building capital ships, the “Speaker” class (Dull,2009). By the time of the Restoration in 1660, Charles II controlled a permanent fleet ofpurpose-built warships commanded by career officers (Rodger, 2005). As the frequency ofwarfare increased after 1700, the Navy expanded. By the 18th century, Britain found itselfat war in one year out of three (Brewer, 1990).

The majority of British government spending – as in other European countries – wasfor war-related purposes (Tilly, 1990; Gennaioli and Voth, 2015). The Royal Navy absorbeda large share of UK military expenditures. Between 1690 and 1810, the Navy grew from147 to 752 larger ships. During peacetime, the Navy typically shrank to a quarter or a fifthof its wartime strength (Figure A1). Of the more than 3,900 unique ships in our database,nearly a fourth (957) were large battleships (known as “ships of the line”). Another 1,024

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were frigates; the rest were smaller, unrated ships typically sailed by lieutenants servingas commanders.

Each individual ship required an enormous expenditure: “Even smaller ships in theEnglish navy of the 18th century cost more than the largest industrial companies had incapital” (Brewer, 1990). Pay for seamen along with the cost of sails, cordage, food, powder,shot, and the spars all added to the expense of running a fighting navy. Royal dockyardsand private yards built and repaired warships, and the Victualling Board bought and dis-tributed provisions for the ships (Baugh, 2015; Allen, 2018).

The Royal Navy was run by the Board of Admiralty, consisting of several Lord Commis-sioners of the Admiralty. The board was composed of both naval officers and politicians;the Board’s president was known as the First Lord of the Admiralty. The Admiralty de-volved many powers and decisions to station commanders and to admirals commandingfleets. Although the UK Cabinet set overall naval strategy, the Admiralty presided over thenaval administrative system. Foreign station chiefs could make appointments, but theseneeded to be confirmed by the Admiralty (Pope, 2013).8 Therefore, a crucial aspect ofAdmiralty power was discretion over officer appointments and assignments – what con-temporaries called ”patronage”:

... power of patronage was the key to the eighteenth-century Admiralty’s au-thority, the one element which counterbalanced weakness to command andnear inability to punish. (Rodger, 1984, p. 245)

2.2 Career progression

Most aspiring officers went to sea at an early age – 10 or 12 was common. Depending ontheir age, they would either join as midshipmen or be promoted to that position from ableseaman or captain’s servant. Training was almost entirely informal; the ship captain wasin charge of organizing lessons in seamanship, gunnery, and navigation. Midshipmenwho had served for six years aboard Royal Navy ships, and who had absorbed all thematerial necessary to fight and sail a ship, could apply for the rank of lieutenant. They werewere then examined by a tribunal of active captains chosen by the Admiralty (Pope, 2013).Although “interest” (i.e., connections) likely affected promotion prospects at the margin,

8There are numerous examples of the Admiralty overturning local station commanders’ recommenda-tions and provisional appointments; there are also many documented cases of the Admiralty forcing ap-pointments on local commanders, picking men who had not been recommended by the local commander(Malcomson, 2007).

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the examination itself was taken seriously. The Royal Navy had no use for lieutenants whowere not highly competent seamen.

Upon receiving a commission, the new lieutenant had to wait for an appointment.Larger ships would carry several lieutenants, and their role varied as a function of se-niority. Lieutenants attended to the day-to-day running of the ship, from readying storesfor long voyages to daily sailing and the command of gun crews. They also kept the ship’slog, which allowed for monitoring the captain (Allen, 2002).

Lieutenants could also be appointed as “Master and Commander.” As such, they wouldbe in charge of a small vessel (typically sloops-of-war with no more than 20 guns). Suchships often sailed with messages or were used to intercept coastal traffic. Command ofeven a small vessel constituted a valuable opportunity to distinguish oneself.9

The decisive step in a naval officer’s career was promotion to post-captain – that is, theofficer in command of a larger vessel. Some lieutenants promoted within a year or two;others had to wait for a long time, or were never promoted. Both performance and con-nections mattered for this consequential promotion, but battlefield performance matteredabove all else: “for a young officer who hoped for command, or for post-rank, nothingwas more swiftly effective than to take an enemy ship of equal or greater force” (Rodger,1987, p. 295). Once appointed as a post-captain, further career progression was by strict se-niority. Initial appointment of post-captains was typically to a sixth-rate or fifth-rate ship,frigates with 20–32 guns and a crew of 150–300. Step by step, captains would then progressto larger and larger ships until they were put in command of a first-rate ship of the line,carrying 80–120 guns and a crew of 900-950 (Baugh, 2015).

If a lieutenant was made “post” at a young age, survived, and continued to serve inthe Navy, he had a good chance to become an admiral. Once they reached the top of thecaptain’s list (with rank determined by seniority), naval officers qualified for promotion toadmiral – first to rear admiral, then to vice admiral, and finally to admiral. Admirals couldalso find themselves without a command (“yellow admirals”), a form of early retirementthat allowed the Admiralty to promote younger men to command fleets and squadrons.

2.3 Success in the Age of Sail

No European navy had a major technological advantage. Frequent captures of enemy shipsdisseminated innovations. Many French-built ships were probably better than British ones

9Although a lieutenant appointed as commander was in effect acting as the captain of a ship, he wouldnot yet have the rank of “captain” – although, out of courtesy, he would normally be referred to as such.

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(Allen, 2002; Rodger, 1987); the Spanish Santısima Trinidad was the largest warship of theage. Naval engagements were decided by the relative size of fleets, by the armament ofindividual vessels in ship-to-ship duels, and above all, by the seamanship, fighting skill,and motivation of captains and their crew.

Despite the similarity of ships, battle outcomes for most of the 18th and early 19thcentury were heavily one-sided. During the Napoleonic Wars, for example, the Royal Navylost only 166 ships (of which five were ships of the line) while inflicting the loss of 1,201ships (159 ships of the line) on its enemies. This “exchange ratio” was a staggering 7:1 onaverage and 32:1 for battleships.10 According to Forester (2012, p. 29), by the early 19thcentury

the British Navy could look back with complacence over a record of victoriesfrequently gained and easily won. Time and time again it had faced numericalodds and had emerged triumphant . . . There had been single-ship actions toonumerous to count, and in the great majority of these actions British ships hadbeen victorious, and often over ships of greater tonnage, with more guns andlarger crews.

Overcoming agency problems among the leaders at sea was key to success. Captains couldeither shy from fighting another ship, or stay out of range with their vessel during a fleetengagement, as happened time and again in every navy during the eighteenth century – orthey could vigorously seek out every opportunity to engage enemy vessels. Navy regula-tions punished lack of fighting spirit (Allen, 2002).11 When effort was deemed insufficient,the consequences could be severe. Loss of a ship brought an automatic court martial, andconvicted navy officers could suffer the ultimate punishment (as was the case with AdmiralByng, executed for failing to capture Menorca).

Ultimately, a captain’s character was more important than rules and procedures:”The Navy... had a real problem of cowardice, and [it] was several times the cause ofserious failures in action... the courage of junior officers and ratings would availnothing if flag officers and captains would not carry their ships into action.”(Rodger, 1987, p. 244)

In addition to the motivation of its fighting men, the Royal Navy could count on a numberof advantages. Professional competence was enhanced by officers selected through exams– commissions could not be purchased.12 Another was a large supply of skilled manpower

10Most 18th-century conflicts resulted in similar ratios; during the Seven Years’ War (1756–1763), for in-stance, the Royal Navy was arguably even more successful than it was during 1793–1815 (Allen, 2002).

11“British commanders were expected to defeat enemy forces much stronger than their own . . . In singleship actions, it was reckoned that a British ship had a good chance against an enemy of 50 per cent greatergun power and crew” (Lavery, 1998, p. 317).

12See Allen (2011) for a general theory of when purchasing commissions works better than patronage.

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from the merchant marine (Allen, 2002). In wartime, recruitment by force (“the press”)was common and ensured that the Royal Navy had first pick of prime seaman.13 SinceBritain often blockaded enemy fleets, her seamen also acquired more experience than theirenemies. There were also no major organizational upheavals, such as the drastic egalitarianreforms that undermined the fighting power of the French Navy after 1793. Finally, thereis some evidence that British crews sustained a higher rate of fire than its foes – the resultof extensive (albeit informal) training.14

2.4 Discretion in promotions in the Royal Navy

Personal connections were crucial for how the Royal Navy recruited its officers. Boys join-ing a ship for the first time often did so through family connections; and promotion to mid-shipman, lieutenant, and post-captain were all affected by who they knew, either throughjoint service or via family connections.

Promotion to post-captain was the crucial step in an officer’s career. Since the risk ofappointing a coward was the main concern of superiors, gallantry in action boosted anlieutenant’s prospects. For example, in ship duels, the lieutenant who boarded the enemyship first was said to ”gain the commission” (i.e. to be virtually guaranteed promotion).Not every lieutenant had a chance to distinguish himself. Because character in the heat ofa naval battle mattered crucially for outcomes, but is also inherently difficult to predict,private information played an important role in making the right decisions.

Naval historians have indeed argued that the use of information derived from personalknowledge (patronage in 18th century parlance) enhanced the performance of the RoyalNavy – it facilitated selection based on ability.15 Such patronage was not a way to privilegethe well-connected, but an important levelling force that facilitated the rise of men fromsimple backgrounds:

...the Navy [contained] a substantial [share] of officers who had risen from rel-atively humble origins, showing that the Service was ... to a large degree a careeropen to talent whereever it might be found. It remains to explain how talent wasidentified and promoted... We are mistaken to suppose that a system based on

13Rodger (1987) analyzes the crews of several ships from the middle of the 18th century and finds that theshare of pressed men averaged 15%. Another 56% were volunteers, and 26% re-enlisted after having been“paid off” for their previous service. The rest of a ship’s company were officers.

14Rodger (1987) cites examples of British warships firing at a rate of one broadside every minute or two.15The modern use of the term patronage – largely synonymous with nepotism and abuse – is fundamen-

tally different from what 18th century practice implies.

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personal influence must ... have chosen unworthy men. This would have beenso if the persons with the power of choice had placed other qualities above pro-fessional ability – . . . choosing officers only from noble blood, as the Frenchnavy normally did . . . a system of patronage to identify and advance men of ability. . . might be at least as efficient as any examination ... in bringing skillful officers tothe head of the profession. (Rodger, 1987, p. 275, emphasis added)

In other words, choosing the next set of fighting captains was crucial. Making the judge-ment call of whether an officer was going to fight to the last or not was difficult; the decisioncould be facilitated by an admiral’s personal knowledge of a candidate. Indeed, some ofthe most outstanding naval officers of the 18th century, such as Horatio Nelson, were pro-moted by close relatives – demonstrating that discretion and performance could go handin hand.16 In section 4, we introduce a conceptual framework that clarifies how and whendiscretion can enhance performance in our setting.

3 Data and descriptive evidence

We now describe the data used in our empirical analysis, their limitations, and the sourcesfrom which the data were derived.

3.1 Personnel and ship data

Our core data are from Threedecks,17 a Web resource listing detailed information on ves-sels, crews, and naval actions. Threedecks constitutes the most comprehensive data sourceon the personnel and ships of the Royal Navy and on fighting events during the Age of Sail.It has assembled information on 25,229 ships, 33,959 seamen, and 1,022 actions and bat-tles among European sea powers (the major ones being British, French, Spanish, Dutch,and Portuguese).18 The dataset is maintained by naval enthusiasts; it is a trusted sourcereferenced by the National Maritime Museum in Greenwich, United Kingdom.

We Threedecks’ complete set of records on the Royal navy to construct our main dataset,restricting the sample to the classic Age of Sail (1690–1849). We restrict ourselves to navalofficers (i.e. lieutenants, commanders, post-captains, and admirals). We then combine the

16Nelson first joined his uncle’s ship, and passed the exam for lieutenant in front of the same uncle whohad risen to Comptroller of the Navy, one of the leading administrators. By age 21, he was already in chargeof a frigate, commanding 200 men (Coleman, 2001).

17http://www.threedecks.org18We extracted the data in September 2018; the numbers are correct as of that date.

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individual-level panel of officers and positions with the ship-level panel to construct amatched “ship–officer” dataset. The resulting ship-level panel contains rich data on out-comes such as the number of actions undertaken, enemy ships captured or destroyed, andwhether the ship itself was captured, wrecked, or sunk.

We conduct a series of validation exercises to assess the coverage and quality of thedata. To evaluate the coverage, we compare the number of rated ships included in our datato the complete record of all rated ships (Colledge and Warlow, 2010). This comparisonyields a coverage rate of 95%. To assess the data quality, we randomly sampled 1% of theofficers and checked their careers against standard references (Clowes et al., 1897; Syrettand DiNardo, 1994). We do not find meaningful discrepancies in the recorded careers.19

Our final dataset contains information on 3,904 ships and on the careers of 5,848 officersover a period of 160 years, a total 82,958 officer-ship-year observations. Figure A2 plots thevariation over time. Unsurprisingly, fighting events cluster during wartime. At the peak,we can reference 500 fighting events per year and connect them to 1,500 officers. Table 1,Panel A shows the summary statistics for the main sample at the officer level. An officerremains in the Royal Navy for an average of 12.5 years and commands a ship for about 6.4years. The average officer serves on 3.5 different ships with an average of 32 guns. Navalofficers in our dataset spend only 18% of their entire service on large battle ships, the shipsof the line. Finally, more than half of all officers make it to post-captain, although few (only3%) ever become admirals.

3.2 Measuring performance

In our setting, performance is generally well-recorded and objectively measured. We com-bine two indicators of success at sea: (i) the capture and (ii) the sinking of enemy ships.Naval officers kept detailed ship logs and reported contact with the enemy in letters to theAdmiralty. Furthermore, events like the sinking of an enemy ship were widely reported.Table 1, Panel A provides an overview of these measures. On average, each officer couldclaim one enemy capture, while only 2% of officers ever sank an enemy ship. Since bothmeasures – sinkings and captures – reflect the success of naval captains, we combine theminto a single indicator of performance, which we call “victories.”

19This is not surprising, as the Threedecks data are based on such historical compilations.

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3.3 Measuring connections

Our analysis focuses on connections to the two top admirals – the First Lord of the Admi-ralty and the Admiral of the Fleet. These two officers were central to all personnel decisions:they promoted lieutenants or confirmed promotions by station commanders;20 determinedwho commanded which vessel and who was put on half-pay; or sent an officer to either adistant and disease-ridden station or a posting near home.

We use genealogical data from the Peerage dataset21 to measure whether officers wereconnected to the Admiralty. This dataset maps the family trees of Britain’s peerage as wellas of the royal families of Europe. It includes genealogical data on the British elite andmilitary. We link officers in our dataset to the Peerage data by matching based on full name,title, year of birth, and year of death. For 11% of officers, the geneological data can be usedto measure family distance to the Admiralty. Given the antiquity of the data, and the factthat many officers rose from the middling classes (and thus are not included in the elitedataset), this is a reasonable match rate.22 Since the family trees of nearly all admirals aredocumented, we can assume that the remaining officers are unconnected to their superior.Throughout the empirical analysis, we include a dummy that denotes whether an officeris matched in the peerage data.

For the subset of matched officers, we compute the shortest distance in pre-determinedfamily ties.23 We then consider an admiral and an officer to have family ties when they areseparated by no more than 16 degrees from either of the two leading admirals (as in Xu(2018)). The measure captures the extent to which two individuals have a shared ancestry.There is a trade-off in choosing a cut-off that defines ”closeness.” Although a low degree ofseparation increases the likelihood of an actual social tie, a low cut-off reduces the numberof admirals and officers who are classified as kin. The cut-off is in line with the enormousweight that contemporaries placed on pedigree and social connections – as evidenced bythe numerous publications listing the family trees of noblemen and -women. The resultsdo not critically depend on the chosen cut-off.24

20In home waters, all appointments were made directly by the Admiralty; its control of overseas promo-tions and appointments increased with time (Rodger, 2005).

21http://www.thepeerage.com22This compares with a match rate of 34% for governors of the British Empire 1854–1966 (Xu, 2018) , who

were recruited from a more elite population.23Pre-determined family ties capture direct blood relatedness through links with earlier generations. These

ties exclude marriages, which form network links endogenously.24Results are robust to cut-offs of between 14 and 22 degrees of separation. Figure A4 shows two distri-

butions. The dashed line shows the distribution in the degrees of separation between pairs of randomlysampled individuals from the peerage dataset (i.e. the elite of England). The solid line shows the distribu-

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Figure A3 shows the share of connected naval officers over time. Although only a fewofficers were linked to the top of the naval administration in the first decades of the 18thcentury, their share increased. It peaked during the French Revolutionary Wars. The pro-portion of connected officers then fell sharply after John Jervis (Earl of St. Vincent), a highlysuccessful career admiral from a middling background, became First Lord of the Admi-ralty; he decided to curtail the role of “influence” in naval appointments.

Out of the 5,848 officers in our dataset, 562 were at some point of their career connectedthrough family ties to the Lord Admiral or the Admiral of the Fleet. Because individualsholding these positions come and go, we observe variation over time in connectedness tothe very top of the Navy hierarchy. Among the 562 officers who were ever connected, 196are connected throughout their career (always connected). For the 366 who experience aswitch in their ties to the Admiralty, the average “switcher” enjoyed ties to the Admiraltyfor 60% of his time on active service.

4 Promoting for performance

We are interested in the selection of promotees by each Admiralty Board. Did they pickmen with greater fighting ability? In this section, we analyse the choice set of each Admi-ralty, and examine the characteristics of those promoted vs. those passed over.

4.1 Conceptual framework

We first introduce a simple conceptual framework to guide the discussion of our empiricalanalysis. We focus on a simplified version but the intuition holds more generally.

There are i = {1, ...N} officers who serve for three periods t = {0, 1, 2}. Officers canserve either in a junior (lieutenant, j = 0) or senior position (post-captain, j = 1). Allofficers start as juniors in period 0 and all agents are promoted to senior positions in period2. The performance of an officer i in period t is given by

yjit = θji + τt + εjit (1)

Performance depends on the unobserved ability of the officer i working in the position j,

tion in the degrees of separation between officers and the two top men at the admiralty. Naval officers andadmirals, if connected, were on much average closer to each other than other members of Britain’s nobleelite. Our cut-off of 16 degrees of separation is equivalent to the closest 20% of pairs, suggesting that theseare relatively close links.

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a time effect τt and idiosyncratic factors εjit. An officers’s ability is thus determined by apair (θ1i , θ0i ) which can vary across positions: some agents are relatively more effective asjuniors, while others are relatively more effective as seniors.

The Admiralty can promote a subset of junior officers to a senior position in period1. We refer to these as “early promotions” and denote those promoted early by di1 = 1.The Admiralty observes period 0 performance at the junior-level, and also holds privateinformation for a subset of officers. We refer to those officers as “connected” and denotetheir status with a dummy ci = 1. We assume that promotion decisions do not affect post-promotion performance other than through the promotion itself: E[ε1it|dit] = 0.

Since we are interested in empirically evaluating the promotion choices, we do not needto take a strong stance on the Admiralty’s objective function. To illustrate the key tensionin our context, however, we assume that the Admiralty promotes officers in order to max-imize a combination of senior-level performance and private benefit:

Promote if E[U |y0it−1, ci] = E[y1it|y0it−1, ci] + αci ≥ νit (2)

The Admiralty will promote an officer i whenever the expected utility from doing so ex-ceeds the outside option νit. This outside option captures the opportunity cost and capacityconstraints in the number of promotions that can be made.

Equation 2 highlights the prediction problem the Admiralty faces. The Admiralty mustpromote based on an officer’s expected future performance in a senior position with the in-formation available at present, namely the observed junior-level performance y0it−1 andthe private information ci. How predictive the junior-level performance is, however, de-pends on the joint distribution of (θ1i , θ0i ). When the link between pre-promotion and post-promotion performance is weak, private information is likely to be more important.

Equation 2 also captures the delegation problem. On the one hand, private informationci can help improve the prediction. This is the efficiency argument for statistical discrim-ination (Fang and Moro, 2011). On the other hand, however, the Admiralty may also bebiased towards the connected officer due to the private benefit derived. The amount of biasis given by α and can capture both taste-based preferences or future benefits received frompromoting a given officer (e.g. a quid-pro-quo). For example, if α → ∞, the Admiraltywould favor connected officers irrespective of their expected performance. To the extentthat connected officers are less effective seniors, such promotions would induce misalloca-tion and lower senior-level performance. Without an estimate of the performance effect ofsuch promotion decisions, it is difficult to assess whether promotions of connected officers

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were due to better information or bias.

4.2 Promotion patterns

To examine differences in pre-promotion characteristics of officers promoted and not pro-moted in a given choice-year, we first construct the choice sets. For each year t, we restrictour data to all unpromoted officers (some of whom are about to be promoted). We furtherrestrict the sample to those years when promotions were made. Out of 160 years in ourdata, promotions were made in 152 years. We create a dummy dit if an officer was pro-moted. The promoted officer then leaves the choice sets of subsequent years. In Table 1,Panel B we report descriptive statistics for each choice-year. In any one year, the meannumber of unpromoted officers is 112, and the mean number of promotions is 18.

We relate pre-promotion officer characteristics to promotions by estimating:

y0it−1 = β0dit + τt + εit (3)

where idenotes the officer and t the choice-year. The dependent variable y0it−1 captures pre-promotion characteristics of the officer. When we look at merit selection, for example, y0it−1is the number of cumulative pre-promotion captures. To ensure that this measure is pre-determined, the pre-promotion characteristics reflect those in the first year the Admiralty-team rotated in.25 With the choice-year fixed effects τt restricting the comparison to onlyofficers within the same choice year, the dummy dit will thus capture the difference inpre-promotion characteristics among officers promoted vs. passed over in the same year.Finally, an officer will remain part of the choice set as long as he has not been promoted orhas not exited. The same passed over officer will thus be observed across multiple years.Accordingly, we cluster standard errors at the officer level i.

Table 2 provides a first impression of promotees’ (pre-promotion) characteristics. Over-all, we observe 5,848 officers; 2,782 of these are eventually promoted.26 In each choice year,we relate the pre-promotion characteristics of lieutenants to whether they were promotedor not. In column 1, the dependent variable is the number of pre-promotion victories.27

The coefficient on promotion is thus an indicator of how “meritocratic” eventual promo-25This avoids concerns of simultaneity, for example that a given admiral promotes and “helps” an officer

with more opportunities to capture at the same time.26Our analysis is based on all officers but also holds when restricted to the subset who was eventually

promoted (Appendix Table A1).27As described, we use the term ”victories” for the sum of captures and sinkings of enemy ships.

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tions were – the larger the coefficient, the larger was the difference in (pre-promotion)victories per year between the promoted and unpromoted officer. Those chosen for pro-motion had, on average, 0.26 victories more per year. The promoted also had slightlyhigher tenure, and they were in command of a vessel for a longer time.28 Officers withmany elite connections, numerous family members who also served in the navy, or whowere connected to the Admiralty were on average more likely to be promoted.

Table 3 examines whether the promotion patterns differ by connectedness. As Equa-tion 2 makes clear, connectedness can either capture better private information or bias.Once again, the comparison is restricted to lieutenants within a given choice year. Thoseconnected to the Admiralty in the year of promotion had captured even more enemy shipsthan other promotees (Column 1).29 Connected promotees had served similar tenure andhad been in command for a similar length of time as unconnected promotees (Columns 2and 3). Connected officers had more elite connections on average, but when it was timefor promotion, those links to the elite did not translate into higher promotion prospects forconnected officers: while those promoted on average had more elite ties than those passedover, connected promotees were less likely to have numerous elite ties than their passed-over peers (Column 4). Finally, connected officers who were promoted are equally likelyto have navy ties as unconnected promoted officers (Column 5).

Promotion to post-rank is an absorbing state, and the factors we examine in Table 3interacted with each other. To visualize the pattern of promotion decisions, we plot simplesurvival curves as a function of (i) connectedness and (ii) performance (see Figure 1). Wedefine ”high performance” as commanders who have accumulated at least two victories.Gray lines indicate the share of unconnected officers who have not yet been promoted,and black lines indicate their connected peers in the same circumstances. In the left panel,Figure 1, dashed (solid) lines represent high-performing (low-performing) officers.

The results show that (a) both connected and unconnected promotees were rewardedfor performance and (b) unconnected but high-performing officers were promoted as quicklyas the connected but average-performing officers. The graph also suggests that the gainsfrom performance are greater for those who were connected: the difference between solidand dashed lines is larger and increases more rapidly for connected than for unconnectedpromotees, consistent with Table 3.

28Lieutenants could serve as independent commanders, or as lower officers on a bigger ship.29In Appendix Table A2 we also show that these higher pre-promotion capture rates for the connected and

promoted officers are robust to the inclusion of choice year and pre-promotion controls.

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5 Estimating selection effects: Main results

How successful were the promotees chosen by the Admiralty? In this section, we assesstheir performance. Promoted officers were markedly more successful than officers passedover for promotion. Theory is ambiguous about how connections affect promotion deci-sions, and thus performance: an Admiral could promote a connected officer due to thegreater predicted post-promotion performance; alternatively, promotions of connected of-ficers could reflect favoritism and bias. Crucially, we show that the Admiralty was partic-ularly good, on average, in picking successful officers from among the lieutenants if theywere connected to leading admirals.

5.1 Empirical strategy

We are interested in assessing how well promotees chosen by the Admiralty perform ex-post. Specifically, we are interested in the selection effect: how well do the promoteesperform relative to those who could have been promoted early, but were passed over? For-mally, we seek to estimate the following selection effect:

τ1 ≡ E[y1it|dit = 1, ci]− E[y1it|dit = 0, ci] (4)

= E[θ1i |dit = 1, ci]− E[θ1i |dit = 0, ci]︸ ︷︷ ︸Selection effect

where y1it denotes the performance of the promoted officer and dit denotes whether the of-ficer was promoted. The selection effect can vary by the amount of private information ci.If the selection effect for connected officers is larger, the Admiralty is using private infor-mation to select better. In contrast, if the selection effect for connected officers is smaller,the Admiralty is distorting the allocation in favor of connected officers.

The key identification challenge is that we only observe the senior-level performanceof those actually promoted, but not the post-promotion performance of those who werepassed over. While we observe E[y1it|dit = 1, ci] in the data, E[y1it|dit = 0, ci] is unobserved.

The gold standard to solve this counterfactual problem is randomization: observe thepromotion choices dit made but then promote officers at random. To mimic the randomiza-tion, observational work typically uses an instrument for promotions that is uncorrelatedwith senior-level performance (Benson et al., 2019; Kleinberg et al., 2018). In our context,however, promotion shocks are invariably tied to performance: spikes in promotions occurprimarily during wartime, when there are many opportunities to capture or sink enemy

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vessels. We thus propose an alternative, difference-in-differences strategy to estimate theselection effect.

To construct a counterfactual, we use the fact that most of those who are passed overin period t are eventually promoted in period t+1.30 That is, their “type” is eventually re-vealed: E[y1it+1|dit = 0, dit+1 = 1, ci] = E[y1it|dit = 0, ci]. Using the eventual post-promotionperformance of officers passed over initially, we obtain:

τ2 ≡ E[y1it|dit = 1, cit]− E[y1it+1|dit = 0, dit+1 = 1, cit+1] = (5)

τ1︸︷︷︸Selection effect

+ (τt − τt+1)︸ ︷︷ ︸Time effects

−E[ε1it+1|dit = 0, dit+1 = 1, cit]︸ ︷︷ ︸History dependence

As Equation 5 shows, a single difference between those promoted early vs. those promotedlate will not identify the selection effect without additional assumptions. Specifically, thereare two threats to identification. The first is the presence of time effects (τt − τt+1). Bydefinition, we are comparing the post-promotion performance at different times at t andt+1. For example, suppose the fast-tracked officer begins the senior position during a timeof war t, whereas the passed over (but eventually promoted) officer is promoted duringpeace time. Even absent a selection effect, it will appear as if the fast-tracked officer didbetter – but that would be driven by differences in the general environment to perform.

Similarly, a threat to identification is history dependence: the possibility that past pro-motion decisions affect eventual post-promotion performance. As an example, supposethose who are passed over are discouraged and thus underperform. If this past passingover also affects performance once eventually promoted, Equation 5 will not yield a con-sistent estimate of the selection effect. As another example, suppose that those promotedlater are given worse assignments and ships, making it harder for them to perform even ifthey were eventually promoted. In both cases, later promotees would appear worse thanthey would have been had they been promoted early.

To obtain a consistent estimate in a simple difference, we thus require (i) the absenceof time effects (τt = τt+1) and (ii) the absence of history dependence (E[ε1it+1|dit] = 0). Thisis rather restrictive. Since our main interest is in estimating the value of private informa-tion, however, we can relax identification assumptions by focusing on the difference inthe selection effect (Equation 5) by connectedness. Since we observe both connected andunconnected promotions in t and t + 1, we can difference out the common time shocks.

30Table A3 shows that those never promoted had characteristics that predict particularly low performancepost-promotion.

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Similarly, we can also difference out the history dependence as long as it does not vary byconnectedness. The assumption for our empirical strategy is thus:

E[ε1it+1|dit = 0, dit+1 = 1, cit] = E[ε1it+1|dit = 0, dit+1 = 1] (6)

Akin to a parallel trend assumption in a standard difference-in-differences, we providecorroborating evidence for the validity of this assumption. Specifically, we show that (i)there is no differential contemporaneous effect of being passed over on performance –those passed over do not subsequently change their performance differentially by connect-edness (Appendix Figure A5) and (ii) there is no differential pre-trend by connectednesswhen comparing the pre-promotion performance of those officers who were passed overbut eventually promoted (Appendix Figure A6).

5.2 Data construction and estimation

To construct the panel dataset, we build on the choice sets constructed in subsection 4.2.We construct post-promotion panels for each choice year t. For those who are actuallypromoted in a given choice year, the post-promotion performance is the actual observeddata. For those who are passed over and only eventually promoted, the counterfactualpost-promotion performance is from the years immediately after their eventual promotion.

To illustrate this, consider Figure 2. Prior to promotion, all officers serve as comman-ders. Each year, they capture a number of enemy ships, indicated by the stars. At time t,the Admiralty promotes officers: A and C are promoted, B and D are passed over. In thisillustrative example, the post-promotion performance ordering is A>C>B>D. The Admi-ralty promotes the more successful (up to time t) officers among the connected and amongthe unconnected. Post promotion, we directly observe the capture rate of A and C on their(post-)ships. B and D continue to serve as commanders, and continue to capture at ratessimilar to their own, earlier performance. At time t+ 1, either another or the same Admi-ralty promotes B and D to the rank of post-captain. They now capture and sink at a new,higher rate. Since we use the later post-promotion performance as a counterfactual per-formance for those unpromoted, we use our data as if they had already begun to captureat time t at their new, eventual higher post-promotion rate.

The resulting dataset is a panel containing the post-promotion performance of eachofficer i in each choice year t during the year after promotion k. Let yitk denote the post-promotion performance of officer i of choice year t in year k after the promotion k ≥ 0. We

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estimate the following regression model:

yitk ≡ yiT (i)k = β0dit + β1cit + β2ditcit + τtk + δ′xitk + εikt (7)

where performance is measured as the number of victories in a given year.31 For each of-ficer i in a given choice year t, the dependent variable takes on the post-promotion perfor-mance from officer i’s respective year of actual promotion T (i) onwards. So if the decisionyear t coincides with the actual year of promotion T (i), we use directly observed data fromthe year in question. If decision year t < T (i), then it is time-shifted data from a later pro-motion. dit is a dummy that is 1 if the officer i was promoted in the decision year t (i.e.dit = 1[T (i) = t]). It is 0 if the officer was passed over in that particular decision year andeventually promoted in a later year t′ = T (i). The dummy cit = 1 if the Admiralty is con-nected to the officer in the year of the decision. τtk are decision year specific dummies foreach year of tenure after the promotion. The vector xitk also controls for ex-post inputs thatmay affect performance. In particular, we control for ship fixed effects and year-specific ef-fects. The standard errors are clustered at the officer-choice set level it, corresponding tothe level of the treatment variation.

If superior information allowed the Admiralty to pick ”winners”, the capture rate ofpromoted captains should be strictly higher than that of passed-over officers. If being con-nected was useful in making decisions because it reduced information asymmetries, theconnected promotees’ performance should also be superior to that of unconnected offi-cers, with whom the leading admirals were less familiar. β0 captures the selection effectamong unconnected officers - the performance difference between promoted unconnected(vs passed over unconnected); β1 captures the selection effect among those passed overwhile connected (vs passed over unconnected); β2 captures the differential gain in selec-tion for those connected. In the presence of private information we expect β2 > 0.

Two additional considerations are worth highlighting. First, since the construction ofthe counterfactual performance for passed over candidates requires us to observe theireventual post-promotion performance, the estimation sample is only restricted to evaluat-ing the selection of the subset of 53% officers who were eventually promoted. To the extentthat those never promoted are likely to be the lowest performing officers, our resultingestimates will provide a lower bound of the overall selection effect.32

31The results are robust to alternative definitions of performance (Appendix Table A4).32Indeed, Table A3 shows that never promoted officers are significantly more likely to share characteristics

that are on average predictive of lower performance as post-captains, had they been promoted.

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Second, the estimand of interest is the selection effect, not the treatment effect of pro-motions as such. We are interested precisely in the non-random variation in promotions,i.e. the way in which the Admiralty chose new post-captains. Equation 5 thus does notcontrol for any ex-ante variables, such as the experience of officers in the choice set or thetype of ships they commanded – we want all observable and unobservable traits to loadonto the actual promotion decision to estimate the overall selection effect.

5.3 Selection effects under discretion

Table 4 presents the main performance results. The baseline specification is shown in col-umn 1. In each year after promotion, those promoted in the choice year outperform thosepassed over (but eventually promoted). Officers promoted by the Admiralty straight awayimprove their capture rate by 0.011 captures a year, about 11% relative to the mean of thedependent variable. This suggests that rapid promotion by the Admiralty favored men ofgreater ability. To ensure that the estimated promotion effect is not driven by differencesin opportunities to perform, column 2 controls for differences in the promotion environ-ment. We constrain the comparison to only promoted and passed over officers who madepost during wartime and for the total (leave-out) number of victories in that year. Bothcovariates are interacted with each post-promotion year. The promotion effect remainsnearly unchanged. In column 3, we allow the promotion effect to vary by connectedness.Connected officers do not outperform to a significant extent once promoted. While un-connected promotees still outperform unconnected, passed-over officers, the difference issmall and statistically insignificant. As the interaction effect promoted× connected shows,however, the selection effect is much stronger among connected officers. It is thus amongthe connected where outperformance is concentrated – promoted, connected officers cap-ture at a markedly higher rate than passed-over, connected officers. This is consistent withadmirals leveraging private information to improve selection.

Those passed over are by definition made post later than those promoted right away.To the extent that being passed over reduces later post-promotion performance (perhapsby reducing motivation), the results may reflect the treatment effect of being passed overas opposed to the selection effect of the promotion. Given our difference-in-differences de-sign, however, this alternative interpretation is only a concern if the treatment effect variesby connectedness. Reassuringly, we do not find that being passed over has a differentialcontemporaneous effect on victories by connectedness (Figure A5). Put differently, we donot observe that being passed over has a treatment effect on performance per se that varies

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for connected and unconnected officers.We can further refine the comparison by including fixed effects that constrain the com-

parison to only those officers made post in the same year (column 4). While this fullyabsorbs the promotion effect in levels, the difference-in-differences setup still allows us tolook at the interaction, which remains nearly unchanged.

Officers can only deliver victories when in command. In column 5, we restrict the sam-ple to only those post-promotion years during which an officer is commanding a ship.33

As column 5 shows, the results are similar: the coefficient is now double that in the pre-ceding column. Relative to the mean of the dependent variable, the gain in performanceis now 23%, nearly identical to the 25% in column 4. Finally, even when given command,differences in allocated ships may explain the estimated effect. In column 6, we thereforeinclude ship fixed effects. Since commanding officers frequently changed, we can distin-guish between officer and ship-specific differences in capture rates. The results remainnearly unchanged, suggesting that ship assignments between promoted vs. passed overofficers do not vary systematically by connectedness.

In Figure 3, we provide visual evidence for the performance gap between promoted vs.passed over officers. The figure shows the selection effect as a function of the years betweenthe immediate promotion and the promotion of the passed over officer. The selection ef-fect is negative for both connected and unconnected, suggesting that – on average – thoseactually promoted indeed made better fighting captains than those who were passed overand only ly promoted. Among the unconnected, those promoted later are performingworse than those promoted right away – but the size of the gap is not a function of howlate promotion occurs. In contrast, among the connected officers, the longer the wait forpromotion, the lower eventual performance is. In other words, the more often a relativeat the Admiralty decided not to promote a related captain candidate, the lower his perfor-mance in the end was. The pattern in Figure 3 strongly suggests that admirals used privateinformation in their selection decisions, and that among the connected in particular, theysucceeded in picking ”winners.”34

33The probability to be given command does not vary by connectedness or being promoted. In AppendixTable A5 we also conduct a bounding exercise. Since being given command is uncorrelated to the indepen-dent variable of interest (Promoted×Connected), the results are virtually identical when imputing differentlevels of counterfactual performance for those who are not given command.

34There is no evidence that late promotees commanded worse ships – the rate and the ship fixed effectsof vessels assigned to later appointees are comparable to those promoted early. The fact that the slope ofthe two lines is different also speaks against a mechanical interpretation – with officers perhaps becomingdemotivated because they were passed over.

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5.4 Capture events and single ship actions

Our results so far suggest that the better performance of connected promotees is not drivenby subsequently receiving better ships or assignments. To go one step further, we use gran-ular data on the fighting power of British and enemy ships. This allows us to study theprobability of winning conditional on a naval engagement, using more than 10,000 obser-vations. Figure 4 provides a simple visualization.35 We plot the probability of the Britishship capturing or sinking the enemy vessel as a function of relative firepower, proxied bythe gun ratio.36 British ships held a sizeable advantage overall. In a straight fight – with agun ratio of 0.5 – victory for the British ship was a virtual certainty. Even when outgunned2:1, British captains fought with no less than an even chance. Panel A on the left-hand sideshows the victory probabilities for connected captains; Panel B, for unconnected ones. Therate of success conditional on relative firepower differed by the group of promotees. Byfar the most successful captains were those promoted by a relative at the Admiralty (”pro-moted connected”). Captains who had been passed over were markedly less successful:At a gun ratio of 2:1, connected and immediately promoted captains won 63% of the time,while the passed over and connected captains only managed 12-18%.

The difference between promoted and passed-over is largest for the connected overmost of the gun ratio range; for the unconnected, performance is more similar. The factthat connected early promotees outperform connected officers ”passed over” by a largemargin suggests that selection was improved by the use of private information. Amongthe unconnected, those promoted faster were only more successful when fighting at a dis-advantage, i.e. with relatively low gun ratios.

So far, we have used data from all naval battles where the enemy and British ship inaction could be identified. Many of these were fleet actions, with numerous warships en-gaged simultaneously. Success could depend on overall naval command, and on spilloversfrom adjacent ships. Our rich data allows us to focus on single ship duels – chance encoun-ters of equally sized ships on the high seas. These duels not only provide chance variationin the matching of officers to enemy ships of different fighting power; they also providea more “controlled” setting in which the outcome – winning, draw, or defeat – can be at-tributed to the performance of the ship commanded by a single captain.

35The regression version can be found in Appendix Table A6.36We define the gun ratio as the ratio of British guns to overall guns in the engagement, adding enemy and

British guns – i.e. with a ratio of 0.5, two ships would be evenly matched. An even more accurate assessmentwould require taking the weight of broadsides into account, i.e. the weight of shot fired by the cannons ofeach side. While available in some cases, using this information would reduce sample size yet further.

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The British Navy dominated in single-ship combat. Of the total of 172 such encoun-ters, British officers captured or sank 115 enemy ships, lost only 16 ships, and engaged in41 inconclusive skirmishes. The British public viewed defeat in single-ship action as espe-cially shameful (Lambert, 2013). The enemy ship’s size (as measured by number of guns orcrew members) in such encounters is remarkably comparable (Appendix Table A7) – eventhough connected promotees typically commanded somewhat larger ships.

Table 5 presents the results for single-ship actions. We implement the research designin the same way as before, comparing the outcomes of single ship actions for officers pro-moted early vs those passed over, broken down by ties to the Admiralty. Consistent withprevious results, fast-tracked officers who had ties to the Admiralty at time of promotionwere more likely to win single ship engagements than those who were passed over andunconnected (Column 1). A single-ship action is deemed won if the enemy ship was ei-ther captured or sunk. Connected promotees are significantly more likely to win: they are24 p.p. more likely (on average) to emerge victorious in a single-ship engagement (column1). Compared with the mean of the dependent variable, this difference is sizeable. To en-sure that the higher capture rate is not driven by more favorable terms of engagement,column 2 controls for the gun ratio (i.e., the ratio of own to enemy guns). Even thoughships with a more powerful broadside were more likely to win, controlling for gun ratiosleaves the gap in winning rate nearly unaffected.

Connected promotees were no less likely to lose an engagement. Their overall highersuccess rate is driven by a smaller number of inconclusive engagements: in essence, con-nected officers either lost or won and never experienced a draw, whereas nearly a fourthof all engagements involving unconnected British captains were indecisive. In single-shipencounters, then, a major determinant of the performance was “fighting spirit” – a will-ingness to fight until victory was won, and the determination to pursue an enemy that wastrying to break off the engagement. The combined results suggests that the Admiralty wasbetter in identifying this “fighting spirit”, leveraging private information.

5.5 Drivers of selection

Connected officers captured more enemy vessels pre-promotion, and they continued tooutperform thereafter. A natural question to ask is how much of this is driven by traits thatare observable (i.e. the publicly known pre-promotion record) vs unobservable (privateinformation or factors unobserved by the econometrician). We examine this question byholding pre-promotion captures and other observable characteristics constant.

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Table 6 adjusts for variation in promotion outcomes driven by observable pre-promotioncharacteristics. Column 1 shows the baseline specification from Table 4, column 4. In col-umn 2, we restrict the comparison to candidates with the same number of pre-promotioncaptures, using fixed effects. As before, connected officers are, on average, no better in bat-tle. It is the connected early promotees who outperform to a significant extent. In column3, we include fixed effects for every level of pre-promotion years of command and tenure.Once again, the estimated differential promotion effect for connected officers remains. Incolumn 4, we include all other available pre-promotion observables (elite and navy ties).As before, connected promotees outperform above and beyond the level that could be ex-pected, given observable pre-promotion performance, service record, elite and naval ties.This outperformance is substantial, increasing capture rates by 25%.

Coarsened exact matching. The analysis so far in Table 6 used fixed effects for pre-promotion observables to capture public information prior to promotion. Our core argu-ment is that the greater success of connected promotees is explained by the Admiralty’sprivate information: if officers who are being considered for a promotion appear observa-tionally equivalent ex-ante, the fact that connected promotions imply more skillful selec-tion ex-post must reflect private information.

Our argument rests crucially on the comparability of connected and unconnected offi-cers based on observables. We will now make officers as similar as possible in terms of thejoint distribution of observable pre-promotion characteristics. We use Coarsened ExactMatching (CEM) (Iacus et al., 2012) to match every connected officer to an unconnectedofficer with comparable pre-promotion traits. CEM is deliberately imperfect – instead ofmatching on precise values, CEM coarsens the distributions of covariates before assigningobservations to strata. While balance of targeted, ex-ante covariates will not be perfect, theprocedure ensures that many ”treated” officers will have a ”control” observation assignedto them. We match officers based on the following properties: (i) officers are promoted inthe exact same choice year (ii) they have an identical fighting record, in terms of enemycaptures and sinkings, up to the time of promotion (ii) they have similar tenure (0-6 years,6-10, 10-16, and more than 16 years), (iii) they have similar experience in commanding ves-sels themselves, and (iv) they have the same number of elite connections. The appendixprovides a more detailed description of the matching procedure.

Our use of CEM differs from other applications in economics.37 Our objective is not toensure that promotion was as good as randomly assigned. Instead, we want promoted officers

37For example Azoulay et al. (2019) uses CEM to ensure that academic fields with the loss of a ”superstar”are compared with identical ones, so that treatment is as good as randomly assigned.

27

to be as similar as possible on all observables prior to promotion to unpromoted officers.What remains are differences in unobservables, which may be predictive of future perfor-mance. The key test is whether connected officers, who were promoted by a relative thatmay have possessed better private information, did indeed perform ”above and beyond”what might have been expected, given every possible dimension of their previous, publiclyobservable track record.

Out of the 17,071 total officer × choice year observations, the CEM routine allows usto match 10,439. The decline in the number of observations reflects the stringent require-ments we impose on matching officers. The resulting estimate is shown in column 5 of Ta-ble 6. After promotion, connected promotees still continue to outperform the unconnectedand promoted. Finally, we can validate the pre-promotion balance on observables using anevent study. In Figure 5, we plot the selection effect (comparing promoted vs passed overofficers) for connected and unconnected promotions around the decision year. As the fig-ure confirms, prior to the year of the promotion decision, there is no systematic differencebetween the promoted and unpromoted in their capture rates. After promotion, consistentwith the regression version (Table 6, column 5), the gap in the promotion effect opens up.While capturing at the same rate as the unconnected pre-promotion, the promoted andconnected subsequently outperform strongly.

5.6 Alternative promotion rules and aggregate impact

Navy promotions are essentially a form of the prediction policy problem (Kleinberg et al.,2015) – admirals are trying to predict officers’ future performance, once promoted, usingboth private and public information. Our setting offers a unique opportunity to considerthe effect of counterfactual promotion rules. For every candidate, we not only observe theirpre-promotion characteristics but also the ex-post performance, once eventually promoted.This allows us to assess the selection effect of counterfactual promotion rules. Importantly,we can also directly gauge the value of discretion by asking whether deviations from agiven counterfactual promotion rule improves or weakens selection.

Formally, consider an alternative promotion rule dAltit = f(y0it−1) that maps a vector

of pre-determined characteristics observed prior to the promotion y0it−1 to the decision topromote officer i in decision year t or not. For example, under a merit based rule, officerswould be ranked based on the number of pre-determined cumulative captures, and theNhighest-ranked ones would be promoted until all slots are filled. We can thus estimate the

28

counterfactual selection effect as:

yitk = βdAltit + τtk + δ′xitk + εikt (8)

where β captures the selection effect of promoting an officer under the given counterfactualpromotion scheme dAlt

it , and the remaining terms are defined as in Equation 7.To ensure the comparability of selection effects, we fix the number of promotions in

each year at the actual total. When promotion rules produce a tie, we break it randomly.To avoid results being driven by particular realizations of such a randomization, we re-runeach counterfactual 1,000 times and report the mean estimate as well as the full distributionto assess the dispersion.

Several assumptions are needed to interpret our results. First, we assume that laterpromotions serve as valid counterfactuals for those who were unpromoted (see section 5).While this assumption is critical for the baseline comparison, we can relax it once look-ing at the relative differences across promotion rules. The second caveat is that our focuson the mechanics of selection abstracts from general equilibrium effects. A merit-basedpromotion system, for example, may have an additional, positive effect by incentivizingperformance. Similarly, a pure seniority-based promotion system will affect selection butmay also disincentivize since it decouples promotions from performance.

Figure 6 summarizes the results. As a baseline, we first consider the selection effectfrom random promotions, abstracting from any incentive responses. We do so by followinga randomization inference approach where we randomly draw promotees in each choiceyear, and repeat the exercise 1,000 times. We then plot the distribution of the estimatedselection effects (red curve). Performance is measured as the (residualized) rate of annualpost-promotion captures per officer. Unsurprisingly, the mean selection effect of randompromotions is centered around 0, with a SD of 0.003. As the estimated distribution alsoshows, the selection reflected in actual promotions is unlikely to be due to pure luck: only 2out of the 1,000 random promotions yields a set of officers that outperforms those actuallychosen by the Royal Navy (Table 4, column 2 - shown as red vertical line).

Connected officers could be higher-performing on average. Our main result would thenreflect the favoured selection of such officers, irrespective of private information. To ruleout this possibility, we also consider a “pure favoritism” rule, where admirals maximizethe number of connected promotions in each choice year.38 Again, we simulate this pro-

38If the number of connected officers exceeds the number of promotion slots, connected officers are drawnat random. Conversely, if the number of promotion slots exceed the number of connected officers, uncon-

29

motion rule 1,000 times and plot the distribution in green. Interestingly, pursuing a “purefavoritism” rule would typically lead to better selection than random promotions. At thesame time, it would result in worse selection than the promotion practice actually used bythe Royal Navy. The mean performance of officers selected according to “pure favoritism”is only 27% of the performance under the actual selection rule. The sign and size of thedifferential are striking. Admirals leveraged their connections to screen their kin, actingas gatekeepers for poorly performing ones.

We also consider two other classic rule-based promotion systems: promotion by senior-ity, and promotion by merit. Seniority-based promotions are a defining feature of manypublic organizations. Its appeal comes from the objective nature of the decision rule. Weassess promotion by seniority by ranking officers in each choice year based on their yearsof tenure, giving strict preference to those serving longest. The distribution of officers’performance implied by strict seniority promotions is shown in dark blue (Figure 6). Strik-ingly, seniority promotions lead to strictly worse selection than promotions at random.This is consistent with negative evidence found in other public sector settings (Bertrandet al., 2019). In our context, promoting based on seniority induces misallocation: thosewith limited tenure but a proven track records would have to wait for promotion insteadof being fast-tracked.

We also consider merit-based promotions. Our measure of merit is enemy captures andsinkings as a commander. The yellow distribution shows how officers chosen by a meritrule would have performed.39 Promotion by strict merit stochastically dominates senioritybased, random, and “pure favoritism” promotions. The mean selection effect of merit-onlypromotions is still 20% lower than the actual promotion effect; 74% of the estimated meriteffects result in inferior selection compared with actual promotion practice.

Navy promotions vs machine learning predictions. How well did the Royal Navy pro-motion practices perform relative to an objective upper bound? We use machine learningalgorithms, which can find and exploit complex interactions in the data, to derive the bestpossible predictions of future performance. In line with recent work in economics (Klein-berg et al., 2018), we examine how much better the Admiralty could have done had it beenable to exploit all available hard data in an objective fashion.

To this end, we use all pre-promotion characteristics to fit a Random Forest algorithm,which allows for non-linear interactions of predictors. The algorithm examines, for a sub-set of the data, which parameters have the greatest predictive power, creating ”branches”

nected officers are promoted at random until the capacity constraint is met.39As before, ties are broken randomly, thus creating a non-deterministic selection effect.

30

based on yes-no decisions conditional on threshold values of the predictor variable. Fig-ure A7 shows an example of such a decision tree. In this case, the algorithm uses 1,116officers and tries to predict victories. At the initial decision node, it splits by victories priorto promotion (more or less than 1.5). At the second node, it exploits information on over-all connectedness of an officer and a higher cut-off for pre-promotion performance. At thefinal level (”leaves”), it has partitioned the sample into eight groups, withN ranging from2 to 761, and predicted performance varying from 1.1 captures post-promotion to 17.4.We do not constrain the number of decision nodes (branches), using 200 different simula-tions of the decision tree (to promote or not to promote). The model’s prediction is thendetermined by the average of decisions across these 200 simulated trees, which each treegetting a ”vote.” Each tree samples from the available dataset a subset, randomly chosen,to ensure that simulations are as uncorrelated as possible (”bagging,” or bootstrap aggre-gation). The actual performance of officers chosen by the Random Forest algorithm is thentested against a 20% ”hold-out” sample of data (not used for fitting the Random Forest)for validation.

To recreate the conditions of actual Admiralty decision-making, we feed the RandomForest algorithm with an expanding sample of observations. For example, the predictionfor the performance of officers promoted in 1771 is based on data for the period 1690-1770 only. As new data arrives, the algorithm is allowed to update decision parameters,as admirals would have done in London – but we do not permit the machine learningprocedure to use future data (from 1801, say) to improve predictions in 1771, for example.

The estimated selection effects are shown as the turqouise line. The post-promotionperformance of promotees chosen by the random forest algorithm stochastically domi-nates all other promotion rules. While not quite on par, actual Royal Navy selection prac-tice was only 27% less effective than the upper bound of positive selection, derived fromstate-of-the-art machine learning procedures – the Admiralty did not make decisions quiteas well as modern machine learning techniques would have done, but they got close. Thisis striking because in other high-stakes settings, such as bail decisions, machine learn-ing approaches have proven superior to human judgment, often by a much larger margin(Kleinberg et al., 2018).

Filtering vs fast-tracking. Why was the actual selection superior to a merit-based rule?Discretion in promotion can work through two margins of adjustment: the admiralty couldchose to promote a lieutenant even if an alternative rule did not favor such a choice (”fast-tracking”). Conversely, admirals could decide that an officer candidate should have to wait– even if according to seniority, or merit, or some other alternative standard, a promotion

31

seems like the right choice (”filtering”).To examine which of these two channels helps to explain the performance of actual

Admiralty promotions, we use strict merit-based promotion as an alternative – the ruleyielding the highest average selection effect among the counterfactual promotion rulesconsidered. Here, dAlt

it = f(y0it−1) is a rule that maps pre-promotion traits - in this case,captures while a lieutenant - y0it−1 to promotions. To decompose the selection effect, weestimate:

yitk = β0dit + β1dAltit + β2ditd

Altit + τtk + δ′xitk + εitk (9)

where the variables are defined as before (Equation 7). We define as ”fast-tracking” apromotion against the rule recommendation dAlt

it = 0 and dit = 1; filtering is converselydefined as dAlt

it = 1 and dit = 0 – passing an officer over although the strict merit rulerecommended promotion. In Table 7, we compare the effect of these two levers, usingvictories per year as the dependent variable. As before, ties in the merit rule are broken atrandom, and we report the estimated mean and standard errors based on 1,000 repetitions.

On average, for both connected and unconnected, merit-based promotions would have”worked,” creating a positive selection effect: when actual promotion decisions followedthe recommendation of the strict merit rule, the resulting promoted officers outperformedthose passed over – as our earlier results imply. For the sample of connected officers, thereis a strong and significant effect on performance from fast-tracking promising young offi-cers that a mechanical merit-based rule could have missed. Filtering – passing over of anofficer despite a positive recommendation by the merit-based rule – also added to perfor-mance for connected officers – on average, relatives who would have been promoted basedon pre-promotion performance but were ignored by their kin at the Admiralty underper-formed. The coefficient on filtering itself is marginally below statistical signficance, but itis different from the effect of fast-tracking. The overall difference between the fast-trackingand the filtering coefficients reflects the advantage conferred by the use of private informa-tion. Importantly, the same pattern is not visible for unconnected officers, where privateinformation was less abundant. Here, neither filtering nor fast-tracking changed perfor-mance significantly – in the absence of private information, deviations from a merit-basedrule did not improve selection.

Aggregate effects. How much did promotion practices matter in the aggregate? To ob-tain a back-of-the-envelope number, we can scale up the estimated annual selection effect

32

by the total number of promotions and average post-promotion years of service.40 Thisimplies that the Royal Navy captured or sank an additional 407 vessels thanks to its pro-motion procedures – instead of promoting at random. This is sizeable and equivalent to10% of actual captures. Compared with strict seniority, the gain is even bigger – a plus of895 enemy ships, or approximately 20% of the total. Merit-only promotions would havebeen inferior to actual practice, too, but only by a margin of 74 ships, or 2% of all captures.Had the Admiralty been able to use modern statistical tools to select captains, it could haveincreased the number of captures even further, by 111 (or 2.6% of total captures).

Again, we abstract from general equilibrium effects – with random, seniority and fa-voritism promotions, lieutenants before their promotion would have arguably tried lesshard, widening the adverse effect of alternative promotion in the aggregate. Conversely, amerit-only system might have increased incentives for pre-promotion effort. Nonetheless,these magnitudes are informative of the advantage the Royal Navy gained by allowingdiscretion in promotions.

6 Conclusion

”the country in wartime [was saved]by giving outstanding men rapidpromotion . . . the right men ended upin the right jobs.”(Pope. Life in Nelson’s Navy 2013)

A central question in organizational design concerns the use of discretion vs rules. Thistrade-off is particularly important in the selection of leaders and other highly skilled per-sonnel when performance is hard to predict. In settings with imperfect information, per-sonal knowledge of candidates can facilitate the use of important, private information. Atthe same time, relying on private information creates scope for favoritism and corruption(Prendergast, 1999).

We study the role of selection in a high-stakes setting: the promotion of officers tocaptains of large warships. Using Royal Navy data for the period 1690-1849, we observethe universe of 5,848 candidates for promotion. We are also able to measure their perfor-mance based on costly actions and tangible results. Since many of the candidates who were

40The aggregate number is computed as: Aggregate captures = Selection effect × Total number of pro-motions × Average post-promotion tenure, where the total number of promotions is 2,782, with an averagepost-promotion tenure of 13.3.

33

initially turned down eventually went on to command, we carefully construct their coun-terfactual performance. This allows us to contrast officers actually promoted and those”passed over” (i.e. promoted later). Based on the individual fighting records of the RoyalNavy officers, we first show that promoted officers outperformed those ”passed over” forpromotion. In making their decisions, admirals gave positive weight to tenure, enemycapture rates, and family relations; on average, they picked ”winners.”

As in other cases of leadership selection (Stogdill, 1974; Northouse, 2018; Cattell andStice, 1954), judging a candidate’s personality was crucial in the Royal Navy. How a cap-tain would perform in the heat of battle was hard to predict, and cowardice was a keyproblem in all 18th century navies. Accordingly, a track record of daring action normallyincreased the chances of promotion (Rodger, 1986). However, few lieutenants could dis-tinguish themselves in independent action; for most of them, the admirals at the top of thehierarchy had to make a momentuous, irreversible decision – promotion to post-captain –based on little ”hard” information.

Did the admirals at the top simply favor their relatives, or use personal knowledge topick the more promising candidates? Each admiralty team had a substantial number ofrelatives to choose from. The ones they actually picked went on to outperform, on aver-age, while the ones they decided to pass over turned out to be distinctly inferior in their(eventual) fighting performance. For unconnected officers, the same pattern holds, but ismarkedly weaker. Even when we use matching techniques to render promoted and un-promoted captains as similar as possible, based on ex-ante available information (i.e. bygiving them the same year of promotion, very similar tenure, and fighting experience),the officers actually chosen outperformed – and especially those related to the apex of thenaval hierarchy. Our results underline the importance of judging ”character.” For example,connected officers were less likely to fight inconclusive engagements with enemy ships –either winning or losing in almost all cases. This strongly suggests that private informationabout the risk-tolerance and fighting spirit of future officers was crucial in picking thosewith the ”right stuff.”

Our paper is the first to show that discretion in promotions can be used to improveselection. Results suggests a surprisingly “enlightened” use of private information in theRoyal Navy. Admirals screened out unpromising kin and accelerated the promotion ofthose who were most likely to be high-performing. This promotion practice was an impor-tant contributor to the Royal Navy’s effectiveness, increasing overall captures by 10-20%.We show that alternative promotion rules – such as strict seniority or strict merit – wereunlikely to outperform the observed promotion pattern.

34

Discretion can enhance performance. This contrasts with existing evidence which fa-vors rule-based hiring and selection, especially in the public sector. However, most earlierempirical work has focused on low-skilled occupations. We argue that discretion is morelikely to be beneficial in the selection of highly-skilled leaders. Also, in a military settingwhere selection is a matter of life or death, the incentives of admirals were closely alignedwith the overall organizational objective. Providing more autonomy in highly competitiveenvironments can be beneficial, allowing decision makers to use private information toimprove decisions.

The results also suggest potential limits to leveraging private information. In our con-text, where we approximate private information by family ties, the potential of private in-formation is constrained by the size of family networks. Transcending the immediate circleof family in personnel decisions has been suggested as a key factor of success in other othersettings (De la Croix et al., 2018). As the demand for personnel increases, organizationsneed to find alternative, scalable selection rules. Indeed, by using machine learning topredict the future performance of naval officers, our findings demonstrate that alternative,data-driven rules could have outperformed the Navy’s actual promotion system.

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Figures and Tables

Figure 1: Promotion hazard rates by performance and connectednessEffect of performance

(Unconnected)

Effect of performance(Connected)

Effect of connectedness(High performance)

Effect of connectedness(Low performance)

0.00

0.25

0.50

0.75

1.00

0 10 20 30 40Tenure (in years)

Unconnected, low perform Unconnected, high performConnected, low perform Connected, high perform

Notes: Reporting the Kaplan-Meier survival estimates for promotion to post-captain (event) as a functionof tenure (time), broken down by connectedness to the Admiralty and high/low performance. High perfor-mance is defined as having captured or sunk more than 1 enemy ship.

40

Figure 2: Construction of counterfactual - illustration

Notes: Illustrating career progression and empirical strategy. We study the promotion of officers from lieu-tenant to post-captain positions. To estimate the selection effect, we compare the (actual) performance ofthose promoted in a given choice-year (Officers A and C) to those who were passed over but eventually pro-moted (Officers B and D). The eventual post-promotion performance at time t + 1 of officers B and D thusserves as the counterfactual performance had they been promoted in time t.

41

Figure 3: Post-promotion performance of promoted vs. passed over officers by years be-tween immediate and eventual promotion, broken down by connectedness

-.3-.2

-.10

.1Vi

ctor

ies:

Pro

mot

ed v

s. P

asse

d ov

er

1 2 3 4 5 6 7 8 9 >=10Years between promotion and eventual promotion of passed over officer

Connected Unconnected

Notes: Post-promotion difference in victories between promoted vs. passed over officers (i.e. the selectioneffect) by years between immediate and eventual promotion, broken down by connectedness to the Admi-ralty. All coefficients are relative to the immediate promotion in a choice year. The sample is restricted tothose always connected (connected at time of decision and time of promotion) and never connected (un-connected at time of decision and time of promotion). The estimates are conditional on commanding andincluding ship FEs (Table 4, column 6). Reporting 95% confidence intervals. Standard errors are clustered atthe officer-decision year-level.

42

Figure 4: Probability of victory by gun ratio for promoted vs. passed over officers, broken down by connectedness

0.2

.4.6

.81

Prob

abilit

y of

cap

ture

.2 .3 .4 .5 .6 .7Gun ratio

Promoted Passed over

(a) Connected to Admiralty0

.2.4

.6.8

1Pr

obab

ility

of c

aptu

re

0 .2 .4 .6 .8Gun ratio

Promoted Passed over

(b) Unconnected to AdmiraltyNotes: Lines are local polynomials for promoted vs. passed over officers, connected or unconnected at time of promotion. The x-axis measuresthe gunshare (of the British ship), defined as gunratio = gunsB/[gunsB + gunsE ], where gunsB and gunsE indicate the number of guns of theBritish and enemy ship, respectively. A gunshare of 0.5 (solid line) indicates a duel between evenly matched battle ships.

43

Figure 5: Performance of promoted vs. passed over officers around decision year, brokendown by connectedness

-.20

.2.4

Vict

orie

s: P

rom

oted

vs.

Unp

rom

oted

-5 -4 -3 -2 -1 0 1 2 3 4 5Year around decision

Connected at t=0 Unconnected at t=0

Notes: Difference in victories between promoted and passed over officers during a five-year window aroundthe year of the Admiralty decision, estimated separately for those connected and unconnected to the Admi-ralty at the time of decision. Treatment (Promoted) and Control (Passed over) officers in each decision-yearare determined by CEM - coarsened exact matching (see Iacus et al. (2012)). We match promoted vs. passedover officers based on their pre-promotion cumulative victories (exact), the choice-year (exact), the total yearsof command (4 bins), pre-tenure (3 bins) and the numbers of elite and naval connections. Reporting 95% con-fidence intervals. Standard errors are clustered at the officer-decision year-level.

44

Figure 6: Selection effect under counterfactual promotion rules

Estim

ated

sel

ectio

n ef

fect

- Ac

tual

pro

mot

ions

010

020

030

040

0D

ensi

ty

-.02 -.01 0 .01 .02Estimated selection effect

Promoted by strict seniority Promoted at randomPromote only connected Promoted by strict meritPromoted random forest

Notes: The mean (and standard deviations) of the selection effects under each promotion rule are as follows.Seniority promotions = -0.0132 (0.0009); Random promotions = -0.0000 (0.003); Promote only connected =0.003 (0.002); Merit promotions = 0.009 (0.002); Random forest = 0.014 (0.001). The solid red line marks theactual selection effect (Table 4, column 2).

45

Table 1: Descriptive statisticsPanel A: Officer level [1] [2] [3] [4]

Mean SD IQR Obs.Years of service 12.54 13.25 15 5,848Total years commanding ship 6.39 5.06 7 5,848Number of ships commanded 3.46 3.24 4 5,848Ship of the line 0.186 0.27 0.33 5,848Guns 32.31 20.46 33.66 5,808Enemy ships captured 1.04 2.23 1 5,848Enemy ships sunk 0.02 0.18 0 5,848Victories (capture + sunk) 0.02 0.18 0 5,848Made post 0.53 0.49 1 5,848Made admiral 0.03 0.17 0 5,848Panel B: Choice year level [1] [2] [3] [4]

Mean SD IQR Obs.Number of officers 112 78 100 152Number of promotions 18.302 18.69 25 152Mean victories 0.126 0.16 0.16 152Mean years commanded 1.378 0.521 0.6 152Mean elite ties 0.285 0.122 0.16 152Mean navy family ties 0.149 0.071 0.104 152Mean share of connected to Admiralty 0.110 0.082 0.157 152

Notes: In Panel A, the unit of observation is the naval officer (i.e., all lieutenants, commanders, post-captains, and admirals). The sample includes all the naval officers who served during our study periodof 1690–1849. In Panel B, the unit of observation is the choice-year, i.e. years between 1690-1849 in whichpromotions were made. We report the mean (column [1]), standard deviation (column [2]), interquartilerange (column [3]), and the total number of officers (column [4]). Elite is the number of noteworthymembers of the public the officer is related to. Naval family is the number of close relatives (father,father-in-law, uncle, grandfather) who were navy officers. A ”ship of the line” is a large naval warship.

46

Table 2: Pre-promotion characteristics of promoted vs. passed over officers[1] [2] [3] [4] [5] [6]

Pre-promotion officer characteristics

Victories Tenure Years commanded Elite Naval family ConnectedMean of dep. var 0.182 10.23 1.758 0.179 0.0906 0.0773Promoted 0.259*** 0.949*** 0.876*** 0.035*** 0.026*** 0.064***

(0.019) (0.164) (0.041) (0.008) (0.007) (0.006)Choice year FEs Y Y Y Y Y YObservations 32,716 32,610 32,716 32,716 32,716 32,716

Notes: The table compares the pre-promotion characteristics of promoted vs passed-over officers. Theunit of observation is the officer × choice year. Victories are the pre-promotion number of enemy shipcaptures or sinkings. Tenure is the number of years since lieutenant exam. Years commanded is thenumber of years commanded. Elite is the number of noteworthy members of the public the officer isrelated to. Naval family is the number of close relatives (father, father-in-law, uncle, grandfather) whowere navy officers. Promoted is a dummy that is 1 if the officer was promoted in a given choice year, and0 if the officer was passed over (i.e. not promoted in the choice year but eventually promoted). Standarderrors (in parentheses) are clustered at the officer level. *** p < 0.01, ** p < 0.05, * p < 0.1.

47

Table 3: Pre-promotion characteristics of promoted vs. passed over officers, broken downby connectedness

[1] [2] [3] [4] [5]

Pre-promotion officer characteristics

Victories Tenure Years commanded Elite Naval familyMean of dep. var 0.182 10.23 1.758 0.179 0.0906Promoted 0.233*** 1.183*** 0.895*** 0.016** 0.013**

(0.019) (0.174) (0.044) (0.008) (0.006)Connected in year of decision 0.000 -3.573*** -0.702*** 0.467*** 0.185***

(0.027) (0.367) (0.123) (0.047) (0.040)Promoted × Connected 0.201*** -0.041 0.196 -0.090** 0.008

(0.066) (0.403) (0.128) (0.040) (0.035)Choice year FEs Y Y Y Y YObservations 32,716 32,610 32,716 32,716 32,716

Notes: The table compares the pre-promotion characteristics of promoted vs passed-over officers andinteractions with connectedness. The unit of observation is the officer × choice year. Victories are thepre-promotion number of enemy ship captures or sinkings. Tenure is the number of years since lieu-tenant exam. Years commanded is the number of years commanded. Elite is the number of noteworthymembers of the public the officer is related to. Naval family is the number of close relatives (father,father-in-law, uncle, grandfather) who were navy officers. Promoted is a dummy that is 1 if the officerwas promoted in a given choice year, and 0 if the officer was passed over (i.e. not promoted in the choiceyear but eventually promoted). Standard errors (in parentheses) are clustered at the officer level. ***p < 0.01, ** p < 0.05, * p < 0.1.

48

Table 4: Post-promotion performance of promoted vs. passed over officers, broken downby connectedness

[1] [2] [3] [4] [5] [6]

Victories per year

Mean of dep. var 0.0970 0.0970 0.0970 0.0970 0.211 0.211Promoted 0.011*** 0.010*** 0.005

(0.004) (0.004) (0.004)Connected 0.009 0.007 0.012 0.002

(0.006) (0.006) (0.014) (0.013)Promoted × Connected 0.023** 0.025** 0.049** 0.036*

(0.010) (0.010) (0.022) (0.019)Choice year × Post-promotion year FEs Y Y Y Y Y YWar controls × Post-promotion year FEs Y Y Y Y YYears between promotions FEs Y Y YCommanding Y YShip FEs YObservations 242,732 242,732 242,732 242,732 111,477 111,413

Notes: The table compares the number of victories per annum of promoted officers to those passed over(and eventually promoted) during each year after the promotion. The unit of observation is the officer× choice year × post-promotion year. The dependent variable, Victories per year, is the sum of enemyvessels destroyed or captured in a given year. Connected is measured as connectedness to the Admiraltyin the choice-year. Promoted is a dummy set to 1 if the officer was promoted in the year of choice, and0 if the officer was not promoted in the given year but promoted later. War controls include a dummyfor war × Post-promotion year FEs and the total number of victories in a year × Post-promotion yearFEs. In columns (5)-(6) the sample is restricted to only those post-promotion years when officers werein command of ship. Standard errors (in parentheses) are clustered at the officer × choice year level. ***p < 0.01, ** p < 0.05, * p < 0.1.

49

Table 5: Single ship duel outcomes of promoted vs. passed over officers, broken down byconnectedness

[1] [2] [3] [4]

Win Draw Defeat

Mean of dep. var 0.656 0.656 0.246 0.0974Promoted -0.050 -0.051 0.070 -0.020

(0.061) (0.060) (0.057) (0.037)Connected 0.078 0.027 0.051 -0.079*

(0.056) (0.057) (0.045) (0.046)Promoted × Connected 0.238*** 0.243*** -0.187** -0.056

(0.088) (0.088) (0.078) (0.061)Gun ratio 0.165*** -0.080** -0.085***

(0.037) (0.033) (0.013)Choice year FEs Y Y Y YObservations 914 914 914 914

Notes: The unit of observation is the officer × choice year × single ship action. Comparing single shipduel outcomes of promoted officers to those passed over (and eventually promoted). The dependentvariable Win is a dummy that is 1 if the British ship won the single ship action; Draw is a dummy that is1 if the single ship engagement was inconclusive; Defeat is a dummy that is 1 if the British ship lost thesingle ship duel. Connected is measured as connectedness to the Admiralty in the choice-year. Promotedis a dummy set to 1 if the officer was promoted in the year of choice, and 0 if the officer was not promotedin the given year but promoted later. Standard errors (in parentheses) are clustered at the officer× choiceyear level. *** p < 0.01, ** p < 0.05, * p < 0.1.

50

Table 6: Post-promotion performance and private information[1] [2] [3] [4] [5]

Victories per year - Post-promotion

Mean of dep. var 0.0970 0.0969 0.0970 0.0970 0.0951Connected 0.007 0.007 0.002 0.006 -0.013

(0.006) (0.006) (0.006) (0.013) (0.013)Promoted × Connected 0.025** 0.022** 0.021** 0.021** 0.029**

(0.010) (0.010) (0.010) (0.010) (0.015)Choice year × Post-promotion year FEs Y Y Y Y YWar controls × Post-promotion year FEs Y Y Y Y YTime between promotions FEs Y Y Y Y YPre-promotion capture FEs Y Y YPre-promotion tenure and command FEs Y YNumber of elite and naval ties FEs YCEM YObservations 242,732 242,683 241,331 241,331 129,976

Notes: The unit of observation is the officer × choice year × year after promotion. Comparing the post-promotion victories of promoted officers to those passed over (and eventually promoted) for each yearafter the promotion. The dependent variable, Victories per year, is the sum of enemy vessels destroyed orcaptured in a given year. Connected is measured as connectedness to the Admiralty in the choice-year.Promoted is a dummy set to 1 if the officer was promoted in the year of choice, and 0 if the officer was notpromoted in the given year but promoted later. In Column 5, treated and control units are determinedby CEM - coarsened exact matching (Iacus et al., 2012). Details of our implementation are explainedin subsection 5.5. Standard errors (in parentheses) are clustered at the officer × choice year level. ***p < 0.01, ** p < 0.05, * p < 0.1.

51

Table 7: Decomposing the selection effect – Fast-tracking vs. filtering[1] [2]Victories per year

Fast-tracking 0.022*** -0.003(Promoted) (0.003) (0.001)Filtering -0.012 0.002(Promoted by merit) (0.009) (0.003)Follow merit rule 0.038*** 0.031***(Promoted × Promoted by merit) (0.014) (0.005)Sample Connected UnconnectedObservations 46,112 195,921

Notes: We regress performance of post-captains on three variables – a dummy of whether they have beenpromoted in accordance with the recommendation of a merit-based rule (”Follow merit rule”), the Ad-miralty ignored a negative recommendation of the merit-rule and promoted anyway (”fast-tracking”), ora lieutenant was passed over despite having a recommendation of the merit-rule (”filtering”). Reportingthe mean and estimated standard errors based on 1,000 repetitions where ties using the merit-based ruleare broken at random. *** p < 0.01, ** p < 0.05, * p < 0.1.

52

A Appendix - For Online Publication

A.1 Additional Tables

Table A1: Pre-promotion characteristics – Excluding those never promoted[1] [2] [3] [4] [5]

Pre-promotion officer characteristics

Victories Tenure Years commanded Elite Naval familyMean of dep. var 0.193 9.576 1.467 0.277 0.138Promoted 0.218*** 1.708*** 1.235*** -0.079*** -0.039***

(0.018) (0.160) (0.039) (0.013) (0.011)Connected in year of decision -0.033 -3.781*** -0.540*** 0.424*** 0.137***

(0.032) (0.376) (0.102) (0.057) (0.050)Promoted × Connected 0.236*** 0.004 0.048 -0.050 0.048

(0.063) (0.337) (0.092) (0.042) (0.038)Choice year FEs Y Y Y Y YObservations 17,070 17,015 17,070 17,070 17,070

Notes: Unit of observation is the officer × choice year. Victories are the pre-promotion number of enemyship captures or sinkings. Sample excludes officers who were never promoted to post-captain. Tenure isthe number of years since lieutenant exam. Years commanded is the number of years commanded. Eliteis the number of noteworthy members of the public the officer is related to. Naval family is the number ofclose relatives (father, father-in-law, uncle, grandfather) who were navy officers. Promoted is a dummythat is 1 if the officer was promoted in a given choice year, and 0 if the officer was passed over (i.e. notpromoted in the choice year but eventually promoted). Standard errors (in parentheses) are clustered atthe officer level. *** p < 0.01, ** p < 0.05, * p < 0.1.

53

Table A2: Pre-promotion performance of promoted vs. passed over officers[1] [2] [3] [4] [5]

Pre-promotion victoriesMean of dep. var 0.182 0.182 0.183 0.182 0.183Promoted 0.259*** 0.233*** 0.157*** 0.234*** 0.153***

(0.019) (0.019) (0.020) (0.019) (0.020)Connected 0.000 0.053* 0.016 0.042

(0.027) (0.028) (0.030) (0.030)Promoted × Connected 0.201*** 0.190*** 0.197*** 0.190***

(0.066) (0.065) (0.065) (0.065)Choice year FEs Y Y Y Y YControls: Tenure, Years commanded FEs Y YControls: Elite, Navy ties Y YObservations 32,716 32,716 32,608 32,716 32,608Notes: Unit of observation is the officer × choice year. Victories are the pre-promotion number of enemyship captures or sinkings. Controls for pre-promotion characteristics are fixed effects for tenure, yearscommanded, number of elite family and naval family members. Tenure is the number of years sincelieutenant exam. Years commanded is the number of years commanded. Elite is the number of notewor-thy members of the public the officer is related to. Naval family is the number of close relatives (father,father-in-law, uncle, grandfather) who were navy officers. Promoted is a dummy that is 1 if the officerwas promoted in a given choice year, and 0 if the officer was passed over (i.e. not promoted in the choiceyear but eventually promoted). Connected is a dummy that is 1 if the Admiralty was connected to theofficer in a given year. Standard errors (in parentheses) are clustered at the officer level. *** p < 0.01, **p < 0.05, * p < 0.1.

54

Table A3: Pre-promotion performance of those never vs. ever promoted[1] [2] [3] [4] [5]

Pre-promotion officer characteristics

Victories Tenure Years commanded Elite Naval familyMean of dep. var 0.182 10.23 1.758 0.179 0.0906Never promoted -0.066*** 1.013*** 0.467*** -0.209*** -0.108***

(0.022) (0.275) (0.074) (0.020) (0.016)Choice year FEs Y Y Y Y YObservations 32,716 32,610 32,716 32,716 32,716

Notes: Unit of observation is the officer × choice year. Victories are the pre-promotion number of enemyship captures or sinkings. Sample excludes officers who were never promoted to post-captain. Tenure isthe number of years since lieutenant exam. Years commanded is the number of years commanded. Eliteis the number of noteworthy members of the public the officer is related to. Naval family is the numberof close relatives (father, father-in-law, uncle, grandfather) who were navy officers. Never promoted isa dummy that is 1 if the officer was never promoted to post-captain in his career, and 0 if the officerwas ever promoted (both in the choice year and eventually in a later choice year). Standard errors (inparentheses) are clustered at the officer level. *** p < 0.01, ** p < 0.05, * p < 0.1.

55

Table A4: Alternative measures of battle performance[1] [2] [3] [4] [5]

Victories per year arsinhBaseline ≥ 1 ≥ 2 ≥ 3 (Victories)

Mean of dep. var 0.0970 0.0560 0.0233 0.00931 0.0678Connected 0.007 0.001 -0.000 0.001 0.002

(0.006) (0.003) (0.002) (0.001) (0.004)Promoted × Connected 0.025** 0.011** 0.006** 0.003* 0.015**

(0.010) (0.004) (0.003) (0.002) (0.006)Choice year × Post-promotion year FEs Y Y Y Y YWar controls × Post-promotion year FEs Y Y Y Y YYears between promotion FEs Y Y Y Y YObservations 242,732 242,732 242,732 242,732 242,732

Notes: Unit of observation is the officer × choice year × post-promotion year. Comparing the numberof victories of promoted officers to those passed over (and eventually promoted) for each year after thepromotion. Victories per year is the sum of enemy vessels destroyed or captured in a given year (column[1]). In column [2], the dependent variable is a dummy for whether the officer capture or sank any ship.The dependent variable in column [3] ([4]) is a dummy if the number of captures or sinkings exceeded 2(3). In column [5], the dependent variable is the inverse hyperbolic sine transformed combined numberof captures and sinkings. variable Connected is measured as connectedness to the Admiralty in thechoice-year. Promoted is a dummy set to 1 if the officer was promoted in the year of choice, and 0 ifthe officer was not promoted in the given year but promoted later. War controls include a dummy forwar × Post-promotion year FEs and the total number of victories in a year × Post-promotion year FEs.The dependent variable in column [1] is the baseline measure of battle performance. Standard errors (inparentheses) are clustered at the officer × choice year level. *** p < 0.01, ** p < 0.05, * p < 0.1.

56

Table A5: Counterfactual performance of non-commanding officers[1] [2] [3] [4] [5]

Battle performanceMean of dep. var 0.0970 0.210 0.0970 0.636 1.174Connected 0.007 0.005 0.007 -0.002 -0.012

(0.006) (0.006) (0.006) (0.008) (0.014)Promoted × Connected 0.025** 0.025** 0.025** 0.025* 0.024

(0.010) (0.010) (0.010) (0.013) (0.022)Choice year × Post-promotion year FEs Y Y Y Y YWar controls × Post-promotion year FEs Y Y Y Y YYears between promotion FEs Y Y Y Y YImputed performance n/a Mean Top 20% Top 10% Top 5%for non-commanding officers 0.246 0 1 2Observations 242,732 242,732 242,732 242,732 242,732Notes: The unit of observation is the officer × choice year × post-promotion year. Comparing the num-ber of victories of promoted officers to those passed over (and later promoted) for each year after thepromotion, imputing different levels of performance for those officers not commanding ships. The de-pendent variable Victories per year is the sum of enemy vessels destroyed or captured in a given year.Connected is measured as connectedness to the Admiralty in the choice-year. Promoted is a dummy setto 1 if the officer was promoted in the year of choice, and 0 if the officer was not promoted in the givenyear but promoted later. War controls include a dummy for war× Post-promotion year FEs and the totalnumber of victories in a year × Post-promotion year FEs. Standard errors (in parentheses) are clusteredat the officer × choice year level. *** p < 0.01, ** p < 0.05, * p < 0.1.

57

Table A6: Probability of victory, promoted vs. passed over by gun ratio[1] [2] [3]

British victoryMean of dep. var 0.975 0.975 0.975Own ship guns / Total guns 0.319*** 0.319*** 0.319***

(0.020) (0.020) (0.020)Promoted -0.006 -0.006 -0.011*

(0.005) (0.005) (0.006)Connected 0.028*** 0.025***

(0.006) (0.006)Promoted × Connected 0.016**

(0.008)Choice year × Post-promotion year FEs Y Y YWar controls × Post-promotion year FEs Y Y YObservations 10,924 10,924 10,924

Notes: The unit of analysis is the officer × choice year × capture event. British victory is a dummy thatis 1 if the British officer captured or sunk the enemy ship. Connected is measured as connectedness tothe Admiralty in the choice-year. Promoted is a dummy set to 1 if the officer was promoted in the year ofchoice, and 0 if the officer was not promoted in the given year but promoted later. War controls include adummy for war× Post-promotion year FEs and the total number of victories in a year× Post-promotionyear FEs. Standard errors (in parentheses) are clustered at the officer × choice year level. *** p < 0.01, **p < 0.05, * p < 0.1.

58

Table A7: Balance table – Single-ship actions[1] [2] [3] [4]

Promoted DiffConnected Unconnected (1)-(2) Obs.

Own guns 35.91 28.58 7.33*** 172(2.58)

Enemy ship guns 31.57 30.49 1.07 166(3.05)

Ratio # own guns / # enemy guns 1.28 1.10 0.17 166(0.11)

Enemy men 268.07 248.70 19.36 128(31.95)

Own capture 0.083 0.088 -0.005 172(0.048)

Enemy capture 0.791 0.556 0.235*** 172(0.080)

Notes: The unit of observation is the single-ship action. *** p < 0.01, ** p < 0.05, * p < 0.1.

59

A.2 Appendix Figures - For Online Publication

Figure A1: Size and fighting power of the Royal Navy, 1690-1849

010

000

2000

030

000

4000

050

000

Num

ber o

f gun

s

050

010

0015

00N

umbe

r of s

hips

1700 1750 1800 1850

Ship count Gun count

Notes: This figure plots the number of British Royal Navy ships (solid line, left y-axis) and total number ofguns (dashed line, right y-axis) over time.

60

Figure A2: Royal Navy size and fighting events

010

020

030

040

050

0To

tal f

ight

ing

even

ts

050

010

0015

00N

umbe

r of o

ffice

rs

1700 1750 1800 1850

Officers Fighting events

Notes: The figure shows the total number of active officers in a given year (solid line, left y-axis) and the totalnumber of fighting events (enemy ship captures and sinking) (dashed line, right y-axis).

61

Figure A3: Promotions to post-captain and share of connected officers

0.0

5.1

.15

.2.2

5Sh

are

of c

onne

cted

offi

cers

050

100

150

Num

ber o

f pro

mot

ions

1700 1750 1800 1850

Post-captain promotions Connected officers

Notes: The figure shows the total number of post-captain promotions (solid line, left y-axis) and the numberof connected officers (dashed line, right y-axis) over time.

62

Figure A4: Degrees of separation in the peerage dataset and among naval officers

0.0

5.1

.15

Den

sity

0 20 40 60Degrees of separation

Connected officers Random pairs in peerage data

Notes: The dashed line indicates the distribution in the degrees of separation between two randomly cho-sen people in the peerage dataset; the solid line shows the distribution between connected naval officers andadmirals. The distribution for naval connections is shifted markedly to the left, indicating that naval connec-tions are relatively close. The graph illustrates that 16 degrees of separation (vertical line) indicates relativelyclose connections.

63

Figure A5: Differential contemporaneous effect of being passed over – By connectedness

-.1-.0

50

.05

.1D

iff c

aptu

res

betw

een

conn

ecte

d vs

. unc

onne

cted

-5 -4 -3 -2 -1 0 1 2 3 4 5Year around being passed over

Notes: This figure shows the differential contemporaneous effect of being passed over between connected vs.unconnected officers for years around the passing over event (centered around 0). For each decision year,we restrict the sample to those officers who were passed over. The coefficients thus show the performancedifference between those connected vs. unconnected in the decision year (i.e. the year they were passedover), around the event of being considered but passed over. Reporting 95% confidence intervals. Standarderrors are clustered at the officer-decision-year-level.

64

Figure A6: No differential pre-trend before eventual promotion – By connectedness

-.4-.2

0.2

.4D

iff c

aptu

res

betw

een

conn

ecte

d vs

. unc

onne

cted

-5 -4 -3 -2 -1 0 1 2 3 4 5Year around eventual promotion

Notes: This figure shows the differential effect of being promoted between connected vs. unconnected offi-cers for officers who were passed over, for years around the eventual promotion event (centered around 0).Reporting 95% confidence intervals. Standard errors are clustered at the officer-decision-year-level.

65

Figure A7: Decision tree - example

Notes: The figure shows predicted values for the post-promotion capture performance of Royal Navy cap-tains. Each bifurcation is a binary decision, based on a single variable’s parameter. The algorithm attemptsto match the data as closely as possible, searching for decision variables and parameters that minimize themean squared error (mse0). In this example, officers with a pre-promotion capture rate >4.5, and with ahigh degree of connectedness to the admiralty (above 60% of the time), have an expected capture rate post-promotion of 17.4 enemy ships; those who captured only one before promotion and were not connected morethan 20% of the time, went on to an average of ”only” another 2.7 victories.

66